Question: The geometric sequence $(a_i)$ is defined by the formula: $a_1 = -\dfrac{9}{2}$ $a_i = -\dfrac{4}{3}a_{i-1}$ What is $a_{2}$, the second term in the sequence?
Solution: From the given formula, we can see that the first term of the sequence is $-\dfrac{9}{2}$ and the common ratio is $-\dfrac{4}{3}$ The second term is simply the first term times the common ratio. Therefore, the second term is equal to $a_2 = -\dfrac{9}{2} \cdot -\dfrac{4}{3} = 6$.